Re: non-homogneous recurrence relation

Re: non-homogneous recurrence relation

I may be coming from a different field, but when we do recurrences in computer science, there needs to be some foundation from which the recurrence begins. It's important to consider the foundation in the event its contribution outweighs the rest of the recurrence.

For example, if T(n) = 3T(n/2) + n, you need to know what T(c) contributes for some small constant value (usually just described as T(0) since the value is irrelevant).

...over lg n many terms. We can reframe T(c) as T(1), after which the summation should be:

$\displaystyle T(n) = -2 \sum_{i=1}^{n} i(cos(n-i)\pi/2))/(n-i)$

EDIT: If we assume T(0) = 0 there's no problem but otherwise you have to add an extra 3^n * T(0) (roughly speaking) to the total for the contribution of the base case, but you didn't say what the base case contribution was. It appears to be substantial, however.

I'm not good at simplification of series with transcendentals (too applied for my tastes) but I assume you can handle it here.